The analysis of macromolecular species in solution by liquid chromatographic techniques is usually achieved by preparing a sample in an appropriate solvent and then injecting an aliquot thereof into a chromatograph. The chromatograph includes fractionation devices of various types that separate the sample as it passes through them. Once separated by such means, generally based on size, mass, or column affinity, the samples are subjected to analysis by means of light scattering, refractive index, UV, viscometric response, etc. For example, in order to determine the mass and size distributions of a particular sample whose separation is performed by size exclusion columns, the chromatograph would measure the sample sequentially by multiangle light scattering, MALS followed by a differential refractometer, dRI. The dRI determines the concentration while the MALS unit measures the excess Rayleigh ratio as a function of angle of each eluting fraction. For molecules very much smaller than the wavelength of the incident light, light scattering measurements at a single angle may often be sufficient.
As each fraction passes through a detection device, it produces a signal often referred to as a “band” or “peak.” Because of dispersion and mixing effects, these bands are broadened somewhat each time the sample passes through a different device. Consider a sample comprised of a low concentration aliquot of a monodisperse protein. In this event, the Rayleigh excess ratio is directly proportional to the molar mass and the concentration. The light scattering signal and the concentration signal should be of identical shape and would overlay perfectly were the two responses normalized to have the same areas. However, as the sample passes from the MALS detector and enters the dRI detector, it passes through intermediate regions and connections that contribute to the dispersion and mixing of the sample. Many sources of band broadening and some of their remedies are discussed in detail by Yau, et al. in their book “Modern size exclusion liquid chromatography” published by John Wiley & Sons in 1979. In the above example, the dRI signal will always appear somewhat broadened with respect to the MALS signals.
The effect of broadening is shown clearly in FIG. 1 which shows a chromatogram of a sample of bovine serum albumen, BSA, in an aqueous buffer along with the computed molar mass, uncorrected for the effects of broadening. The uncorrected molar mass is shown in trace 1. It is presented divided by the molar mass of the monomer, Mw0, so that the vertical axis for the monomer reads 1, the dimer reads 2, etc. Trace 2 corresponds to the 90° light scattering signal as a function of time. Trace 3 corresponds to the dRI signal. The aggregation states have been fractionated so that the rightmost peak region, from 16 minutes to 18 minutes, is data from the pure monomer, from 14 minutes to 16 minutes is from the dimer, etc. In each peak, broadening causes the concentration at the center of the peak to be suppressed and that in the “wings” to be enhanced. Combining this broadened dRI signal with the MALS signals to determine molar mass at each elution time causes the molar mass determined near the peak's center to be systematically overestimated, while that in the wings to be underestimated. The situation reverses when the concentration detector is upstream of the MALS detector. This gives rise to the non-constant molar mass data within each peak region. If there were no band broadening, the data would consist of a series of plateaus at 1 for the monomer, 2 for the dimer, etc. As the fractionated sample becomes more polydisperse, the effects of band broadening become less apparent (but are still present). For a well fractionated sample comprised of discrete aggregate states, the problem is obvious. In FIG. 1, the monomer peak is well resolved so the broadening problem is clearest. The aggregates are progressively less well resolved so they show the problem to a lesser extent. In order to compensate for these distortions, a variety of methods have been employed. Most are based upon the work of L. H. Tung presented in his 1969 paper published in the Journal of Applied Polymer Science, volume 13, p 775 et seq. The afore-referenced book by Yau et al. discusses some of the means to correct band broadening. Throughout the chromatography literature, many papers address means to perform these corrections, i.e. to restore the broadened band to the shape it would have had were no broadening sources present. Most of the techniques are numerically unstable and can result in physically unreasonable results, such as negative concentrations, or negative scattered intensities, and therefore are rarely used. The characterization of proteins by MALS measurements represents an area of particular importance, yet even here, band-broadening corrections are rarely seen because of the difficulties associated with their implementation.
Band broadening effects occur in a variety of multi-detector implementations of liquid chromatography. For example, if a sample is to be measured by an on-line viscometer so that its intrinsic viscosity may be determined, then a dRI will also be needed. As the sample passes from the dRI to the viscometer, it will experience band broadening resulting in a spreading of the specific viscosity curve with respect to the concentration curve derived from the dRI measurement. Again, the computational difficulties, associated with restoring the broadened signal to conform to what it would have been without broadening, often result in questionable results, especially if the samples are indeed monodisperse such as unaggregated proteins.
It is the purpose of the present invention to provide an analytical method by which band-broadening effects may be corrected in software with both ease and precision. Another objective of the invention is to provide a new approach to such corrections whose departure from the conventional approach is sharply distinguished therefrom. The present invention is expected to be of greatest utility for the analysis of separations of protein samples. A consequence of this application will be the more precise characterization of protein conjugates as well as aggregate states. A further application of this invention is its ability to improve the determination of intrinsic viscosity measurements by correcting the band broadening effects associated with the sample passage between a concentration detector and a viscometer. An important application of the invention will be its application to the rapid determination of the 2nd virial coefficient of an unfractionated sample as discussed, for example, in U.S. Pat. No. 6,411,383 and U.S. Pat. No. 6,651,009, by Trainoff and Wyatt. The successful implementation of that method depends critically upon the ability to determine accurately the square of the concentration at each elution volume. This requires an accurate measurement of the concentration at each such elution volume. The latter determinations are made generally on unfractionated samples whose detector responses are a single peak whose mass composition is the same at each interval collected. This single peak is broadened as it proceeds through the series of detectors leading to systematic errors in the derived results, unless the effect of broadening is corrected.